Generating High-Quality Logical Question-Answering Data for Large Language Models Using Operations Research Techniques

Logical reasoning is a foundational capability in large language models (LLMs). High-quality data is essential for enhancing the reasoning capabilities of LLMs through both pretraining and fine-tuning. With extensive use of publicly available internet data and copyright disputes of using data sourced from books or examinations, synthetic data is increasingly recognized as a valuable alternative. We introduce Operations Research Aided Synthesis (ORAS), a novel framework that leverages operations research techniques to systematically generate high-quality evaluation data. By synthesizing rigorous training examples, ORAS not only enhances the logical reasoning abilities of LLMs but also enables more reliable performance assessments. The proposed method integrates mathematical programming methods to generate question-answer pairs. ORAS employs a dual-phase approach: the first phase uses optimization algorithms to construct and evaluate the logic systems by solving the problem using a mathematical solver. The second phase translates the logic system to natural language descriptions, and generate answers according to the information from the mathematical solver. Using data generated from ORAS, fine-tuned models improved by 38% for Qwen-7B.